US faces new tasks in Mideast.

By Geoffrey GodsellStaff correspondent of The Christian Science Monitor

President Reagan's victory in the Senate vote on AWACS will help to preserve among United States allies what they see as the credibility of American commitments.

At the same time, it will give the Reagan administration a measure of maneuverability, which it might otherwise have lost, in dealing with the most urgent problems in the Middle East.

For the administration, the most pressing needs are:

* A firm and steady hand on the relatively narrow issue of ensuring that Israel completes its final withdrawal from Sinai by April 26, as laid down in the Camp David accords. Egyptian President Hosni Mubarak requires this to justify his continued commitment to Camp David.

* An equally firm and steady hand on the issue of ''full autonomy'' for the Palestinians, as promised in the Camp David accords. To date, Israeli Prime Minister Menachem Begin's hard-line government has shown itself more interested in annexing the West Bank (where most Palestinians are concentrated) than in any meaningful autonomy for them.

* A sensitive but steady hand in moving forward from the AWACS deal with the Saudis to filling in the overall blueprint for a strategy to defend the Gulf area against any Soviet threat - the strategy to be based on bilateral agreements with Saudi Arabia, Egypt, and Israel.

* An equally sensitive yet steady hand in dealing with Israel's shock at the defeat of those who opposed the AWACS deal (including itself) and Israeli fears about survival roused whenever the US is perceived as tilting away from Israel and toward the Arabs.

* A flexible but steady hand in encouraging rapprochement between the post-Sadat Egypt of President Mubarak and other moderate Arab states, particularly Saudi Arabia. This may involve a positive US interest in Saudi Arabia's eight-point Middle East peace plan, once Israeli withdrawal from Sinai has been completed in April - something that Israel would vigorously oppose.

The opportunities and dangers for the US have been increased by the fluidity introduced into the Middle East by the assassination of President Sadat and his being succeeded by the relatively unknown and yet-to-be-proven Mubarak.

Away over the horizon to the northeast, the Soviet Union is pushing and probing diplomatically to try to regain admission center stage as a superpower with a legitimate right to a say in the Middle East.

On the periphery of the area to the west, Libyan leader Muammar Qaddafi continues to cause uncertainties in Chad. And farther west still, Muslim fundamentalists are at work in a shaky Tunisia; and King Hassan of Morocco is in trouble both on his home front and with the Polisario guerrillas in the Western Sahara.

As for the AWACS vote, it has come in a week that the Saudi government must consider unusually propitious for itself. As the Saudis see it, an American President has for once stuck to a commitment to them and outmaneuvered Israel and the pro-Israel lobby in the US. And at the current OPEC meeting in Geneva, Saudi Arabia has at last been able to reassert its primacy among oil exporters and become once again the pacesetter for a unified oil price. (OPEC agreed Oct. 29 to the Saudi proposal of $34 per barrel. The top price for high grades of oil was set at $38 per barrel.)

Both developments underline the potential diplomatic clout that Saudi Arabia now has - and particularly with the US. Nobody views this with more concern than Israel, with Israelis feeling they have more to lose than anybody else if the changing pattern is not halted.

The Israelis have been in a difficult position from the outset. If they succeeded in their efforts to thwart the AWACS sale to the Saudis, they knew that there was a danger of an upsurge of anti-Semitism in the US. (Hence the low profile which Israeli spokesmen and Jewish Americans have maintained in recent weeks.) But if the sale went through, they knew - as an unusually somber Ephraim Evron, Israeli ambassador to the US, said on NBC television Oct. 29, it represented a change in the balance of power in the Middle East.

In Israel, Prime Minister Begin said of the US Senate vote: ''A new and grave danger now faces Israel.'' He added delphically and ominously that Israel would do whatever it had to do to deal with the changed situation.

Mr. Begin gave no clue as to whether he was thinking of military or diplomatic action. As things now stand, Israel holds hostage both the West Bank and that last segment of Sinai due to be returned to Egypt in April. And if military action is contemplated, Israel has shown no reluctance in the past to precipitate crisis in south Lebanon.

Whether President Reagan's latest letter to Mr. Begin will calm the latter's fear and anger remains to be seen. In it, Mr. Reagan promised to help Israel maintain its present military and technological advantage.

Helena Cobban reports from Cairo:

News of the White House's success in winning Senate approval for the Saudi AWACS deal divided the Arab world clearly into pro- and anti-American camps.

First reactions were enthusiastic, not only in Saudi Arabia itself but also in Egypt and from some quarters in Jordan.

Meanwhile in Lebanon, the Communist Party daily Nida called on radical Arab states to ''expose and resist'' US plans in the region.

In Saudi Arabia, where all press organs receive government backing, the daily al-Jazirah described the Senate vote as marking, ''a turning point in US relations with Saudi Arabia, the Arabs, and Israel.''

''We must congratulate ourselves and our friends in the US that the Saudis have been able to achieve a big political victory for Arabs everywhere,'' the paper said.